Volume 25, pp. 201-205, 2006.

On norms of factors of multivariate polynomials on convex bodies

András Kroó

Abstract

Estimation of norms of factors of polynomials is a widely investigated extremal problem with numerous applications in functional analysis, number theory, approximation theory. In this note we study the following problem: let $K$ be a convex body in ${\mathbf{R}}^d$ and consider a product of polynomials $qr$, where $q$ is arbitrary and $r$ is a monic multivariate polynomial. The goal is to find an upper bound for the uniform norm of $q$ on $K$ provided that such bound for $qr$ is known.

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Key words

multivariate polynomials, norms of factors, convex bodies

AMS subject classifications

41A17, 41A63